If you have ever played the Witcher III you know exactly what this is. If you haven't, go pick it up on gog.com it is worth the cost.
Regardless, psychological choices is when you give your players free choice to make a decision that will have a lasting impact on the gaming world in which they are playing.
You can make these decisions a choice between two seemingly bad or good choices. I will say that it is easy to choose between a good vs evil choice, but what if you have to choose between saving a person with something that could kill them or letting them die? That is a minor side quest in the Witcher III. If you choose to save the girl, you find out much later while randomly walking into an army camp that she is alive but non-verbal and unresponsive. Her husband wishes you had let her die and one day he may have to kill her to be free. It is a gut punch.
Listen to find out other ideas of implementing this into your game.